Unit Two: Changing Views of the Universe

Part 1: From Ptolemy to Copernicus

In this section students can explore the change of perspective in how scientists viewed the universe through the Renaissance. This can truly be called a paradigm shift, as not only science was impacted but also religion, philosophy, and psychology.

1. The Ptolemaic Universe.

Claudius Ptolemy was a Greek Egyptian of the first and second centuries C.E. He was a mathematician and astronomer–though his astronomy was not easily distinguishable from what we identify as astrology. Ptolemy?s universe is geocentric (“earth-centered”). That is, the earth stands immobile at the center of the universe while the planets and stars orbit around it. Ptolemy did not so much “discover” the geocentric model of the universe as codify it. His work on astronomy/astrology, Almagest, served as textbooks through the Renaissance. It is important when bringing this information to students to not jump to the conclusion that Ptolemy and his colleagues were benighted idiots, unenlightened by The Discovery Channel: cultural hubris is a sin to be avoided. What is important is that these scientists were seeking an order in the universe and trying to make sense of it. And it did make sense.

More properly known as the "anatomical man," this beautiful image is from Jean, Duke of Berry's Tres Riches Heures.

Students may find as particularly intriguing the ideas of the macrocosm (“big world”) and microcosm (“small world”) utilized by Ptolemy and many natural philosophers through to the Renaissance. According to this view, the universe–the planets (including sun and moon), the stars (the constellations of the zodiac in particular) and the earth–represented the macrocosm. The planets and stars were thought to travel along crystalline spheres (people could not imagine anything that could keep these bodies from falling to the earth otherwise). This large world was reflected in the microcosm; and correspondences between the signs of the zodiac and parts of the human body, between the planets and organs served as the basis for not only astrology but primitive medicine and psychology.

2. The System of Copernicus.

Nicolas Copernicus was an unassuming church canon, mathematician, and astronomer. He was not the type of person one would expect to shake the very foundations of his world and his church. And, at least while he lived, he did not.

Copernicus’s contribution to astronomy is, of course, his introduction of a heliocentric (“sun-centered”) model of the universe. He still believed in the crystal spheres and that the planets maintained circular orbits, but he was on the right track.

Suggested artistic activities:

  • Draw an illustration of the “starry man”: The Macrocosm and the Microcosm. The macrocosm and microcosm were illustrated In many almanacs and books of days of the Renaissance. That found in Jean, Duke of Berry’s Tres Riches Heures is particularly impressive.
  • A “movable” picture of the Ptolemaic and Copernican universes. In this simple project students will use compass and straight-edge, color, and artistic sensibility to beautifully illustrate. Depending on the need of the teacher, size and dimensions of the picture may be changed. (See left).

Print sources:

Arthur Koestler, The Sleepwalkers: A History of Man’s Changing Vision of the Universe, Penguin, 1990.

The Très Riches Heures of Jean, Duke of Berry (facsimile edition), George Braziller, 1969.

Part 2: Johannes Kepler

Of all the fascinating astronomers of the Renaissance, Johannes Kepler may be the most interesting. A mystically-inclined with poor eyesight and who suffered from piles, he nevertheless was an imposing intellect and perhaps the first modern scientist. He possessed a rich imagination, incredible mathematical ability, and the courage to disagree with even his most dearly held beliefs.
Kepler?s first discovery in regards to astronomy occurred to him in a moment of inspiration while he was teaching geometry. He was giving a lesson on the so-called “Platonic solids,” the five regular solid three-dimensional shapes with identical edges and faces also known as the cube, the icosahedron, dodecahedron, tetrahedron, and octahedron. Plato’s mystical speculation about the solids included associating the different figure with the elements known to ancient philosophy. Following Pythagoras, Plato associates the cube with earth, the icosahedron with water, the tetrahedron with fire, the octahedron with air, and the dodecahedron with ether or the quintessence. As Kepler was teaching he recalled Plato’s discussion of these figures in the Timaeus and how the great philosopher described the planets as correspondent to the regular solids. Kepler intuited that Plato was right and set about to prove it geometrically and mathematically. He came very close.

Kepler Sphere

A famous image of the Platonic solids "nested" inside one another in Kepler's imagination of the universe.

Kepler held to the heliocentric model of the universe–though he thought Copernicus was in error concerning a few parts. Kepler presented his findings in his book Mysterium Cosmographicum (1596). In the book, Kepler describes a sphere circumscribing a cube, the sphere corresponding to the orbit of Saturn. Inscribing the cube is another sphere, which would correspond to the orbit of Jupiter. The sphere of Jupiter circumscribes a tetrahedron. Inscribing the tetrahedron is another sphere, which corresponds to the orbit of Mars. Mars’ orbit circumscribes a dodecahedron. Inscribing the dodecahedron is yet another sphere, upon which is the earth’s orbit. This sphere circumscribes an icosahedron, and inscribing the icosahedron is a sphere which corresponds to the orbit of Venus. Finally, inscribing the icosahedron is another sphere correspondent to the orbit of Mercury, inside of which is an octahedron, which surrounds the sun. Kepler did not imagine that these shapes were banging around the heavens, nor did he hold to the idea of physical crystalline spheres; what he was exploring here were ratios. The weird thing is that he was really close. (See items).

Kepler’s discoveries drew the attention of Tycho Brahe, a Danish astronomer and eccentric (Brahe lost his nose in a knife fight as a young man and had several different “noses” made from different metals (one for every occasion one might assume!). Kepler was mostly interested in gaining access to Brahe’s research. Brahe had Kepler cool his heels working on pinpointing the erratic orbit of Mars. Brahe had no truck with the heliocentric model of the universe favored by Kepler, but maintained a belief in his own system in which the sun and moon orbit the earth while the rest of the planets orbit the sun. He was his own man.

Through his work on Mars, Kepler eventually concluded that the orbits of the planets could not be spherical. Sometimes the planets moved faster than at other times, sometimes slower. In his first law, Kepler concluded that the planets must have elliptical orbits; in his second that the radius vector sweeps out equal areas in equal times; in his third law, he states that the squares of the periods of the planets’ revolutions are as cubes of their mean distances from the sun. And all without a calculator!

Kepler did not want the elliptical orbits to be true–he much preferred the aesthetic and philosophical beauty of the Platonic solid model–but he had the courage to admit the truth.

Possible artistic activities:

  • A Mobile of the Platonic solids  Using painting paper, colored card stock, or what have you, students can make mobiles of the regular solids using their geometric skills. While the shapes are still in two-dimensional form, students could illustrate or paint each shape according to its corresponding element. How would one represent fire? Earth? Air? Water? What is ether?
  • Kepler’s Universe: Platonic Solid Nesting Boxes  For older or more advanced students. Have students try to duplicate Kepler’s process. How big should each figure be? How can they fit inside one another? This could be done with painting paper, card stock, or, for the very intrepid, Plexiglas. If using Plexiglas, copper tubing could be used to illustrate the orbits of the planets. Challenging, but rewarding!

Part 3: Galileo and the Telescope

In this page of a seventh grader's workbook, we see Galileo's first telescope experiment (often called the optical bench) demonstrated. In addition is a diagram of Galileo's work with pendulums.

Galileo Galilei, known as “the wrangler” to his fellow students during university days, was an incredibly inquisitive person, blessed with an incredible intellect but cursed with a tremendous chip on his shoulder. Many of his discoveries in physics might be explored: for example, his work with the pendulum clock and discovery of the law of the pendulum; his experiments refuting Aristotle on the time falling bodies take to fall. In this unit, following up on the work with the camera obscura, I choose to focus on his work in optics, telescopes, and astronomy, all of which are closely connected with one another. Making a telescope. After telling the students a brief overview of Galileo’s early life, the teacher should introduce them to Galileo’s work with telescopes. Galileo did not invent the telescope; he heard about the Dutch invention of this technology and decided to make his own. His telescopes were cutting edge technology for the time, though their power was very weak by modern standards. When he pointed this device at the heavens he saw wonders–and eventually wound up in a lot trouble. Unfortunately, when asked exactly how his telescope worked, Galileo could not give a definitive or convincing answer.
Suggested artistic activities:

  1. Making a yardstick telescope (optical bench).
    Using simple tools (yardstick, stands, lenses, and lens holders) students can make a simple telescope and observe local phenomena.
  2. Making a diagram of the telescope. Make sure to include the reversal of the image.
  3. Illustrations of Galileo’s astronomical discoveries.
    Galileo was the first to see solar flares, the rings of Saturn (though, because he was not using a strong enough magnification, he thought they were planets), the mountains of the moon, sunspots, the phases of Venus, and the moons of Jupiter. When he trained his telescope on the Milky Way, he saw more stars than he could ever have imagined.
  4. A letter.
    Students could imagine a letter that Galileo, someone in his family, or one of his contemporaries might write concerning Galileo’s work and his trouble with authority. What are some of the struggles he may have felt? What was the cause of his trouble? Was it simply a case of oppression? Was he asking for trouble?

Print Sources:

Arthur Koestler, The Sleepwalkers: A History of Man’s Changing Vision of the Universe, Penguin, 1990.

Dava Sobel, Galileo’s Daughter : A Historical Memoir of Science, Faith, and Love, Penguin, 2000.

Arthur Zajonc, Catching the Light: The Entwined History of Light and Mind, Oxford University Press, 1993.

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